26 research outputs found
Measuring population threshold from fluorescence intensity as a function of the field strength for a given duration.
<p>(A) Fluorescence intensity measured using calcium imaging, from about 100 neurons in the 1D culture that are within the field of view of the microscope. CNQX, APV and bicuculline were used to completely disconnect the network. External stimulation was given at times marked by the vertical grey lines. The four blue curves show typical fluorescence responses of the network, with excitation seen as a sharp increase in fluorescence intensity. The number adjacent to the grey line represents the amplitude of the stimulating signal (in volts). (B) At a fixed pulse duration, the intensity of the normalized fluorescence vs. voltage used for stimulation is a cumulative Gaussian distribution. The mean minimal amplitude needed for stimulation (āStrengthā) was obtained by fitting each experimentally measured fluorescence intensity as a function of the electric field amplitude to a cumulative Gaussian distribution (the Error function) and extracting the expectation value of the Gaussian, The half maximum of this curve is thus taken as the threshold for excitation of the neuronal population.</p
Apparatus used to stimulate neuronal cultures with external electric fields.
<p>(A) Waveforms of the measured applied voltage between the electrodes (upper row) and within the fluid (lower row), approximately at the center of the experimental cell where the culture is located. Left column is for pulse durations of 1ms and the right is for durations of 100 Ī¼s. (B) The plastic insert with one pair of electrodes used to stimulate the neuronal culture. The electrode wires are indicated in the picture by arrows. A plastic rim extending into the medium locates the two parallel platinum wire electrodes about 1 mm above the culture. (C) The device used to stimulate the neuronal culture with two orthogonal pairs of electrodes. A plastic rim holds two pairs of platinum electrodes about 1mm above the culture, which are denoted in the picture by arrows. (D) Sketch of the electrical circuit for a pair of electrodes that is driven by a single square pulse with varying durations. The electric field created between these electrodes is used to stimulate a neuronal network cultured on a glass coverslip. (E, F) Sketch of the electrical circuit for two pairs of electrodes that are fed with separate single square pulses with varying durations (synchronized but with no common ground). Changing the relative amplitudes changes the orientation of the electrical field, which is used to directionally stimulate a neuronal network cultured on a cover slip. (G) Sketch of the electrical circuit for obtaining a rotating electric field. Two pairs of electrodes are each fed with one cycle of sine or of cosine voltage pulses (i.e. two signals with the same amplitude but phase shifted by Ļ/2).</p
Angular dependence of minimal durations and amplitudes needed for exciting a connected 1D culture with varying angles with respect to the linear culture.
<p>(A) A typical example of an experiment with constant amplitude (Ā±22 V) and varying pulse durations. The pulse duration is represented by the distance from the center of the circle. In this example a square pulse of 400 Ī¼s was needed to excite with the field perpendicular to the lines (90Ā°), while only 150 Ī¼s was needed for excitation parallel to the lines (0Ā°). (B) Fixed amplitude results averaged over 15 different cultures. To allow averaging, the pulse duration in each experiment is normalized by the duration needed to excite the culture in 90 degrees and is plotted as the distance from the center. The red star represents the average, and the black crosses the standard error. The angles are āfoldedā to the first quadrant (e.g. 330Ā°ā30Ā°). (C) A typical example of an experiment with pulse duration held fixed while the amplitude is varied. The distance from the center of the circle is now the amplitude of the square pulse (in Volts) needed for excitation of the culture. The duration was held constant throughout each experiment and was determined as the minimal duration needed for the excitation at Ā±22 V for 90Ā° orientation. (D) Average over 5 different cultures. The red star represents the average, and the black crosses the standard error. The amplitude of each experiment is normalized by the amplitude needed for excitation at 90Ā°. Inset: Schematic for the setup with 1D networks. The 1D culture is grown on thin lines (width 170 Ī¼m, length 11 mm). An external voltage is applied by two perpendicular pairs of bath electrodes, driven by two separate power supplies. The ratio between the amplitude of each pair of electrodes determines the angle of the electrical field allowing measurement of different angles without the need to manually rotate the culture.</p
Effect of placing the CMS and DRL electrodes at different locations relative to the TMS coil.
<p>(A, B, C) Recordings from electrodes F4 and C6 (triangles) for TMS application at C2 (cross) are shown for different placements of the CMS (circles) and DRL (squares) electrodes. Different colors correspond to different placements of CMS-DRL (red = standard positions assigned on the Biosemi cap, green = P3-P7, blue = CP3-TP7, pink = C3-T7, cyan = FC3-FT7, yellow = F3-F7). (D) EEG traces after TMS stimulation at time 0 with the CMS and DRL electrodes placed on the index finger of the left hand. The corresponding electrode wires had a minimal distance of 50 cm from the TMS coil. The points of stimulation consisted of Cz, CPz, and POz. Shown are 13 trials with 13 electrode traces each acquired at 16 kHz. The red traces correspond to the raw, unmodified electrode traces. The green traces correspond to the same data where in addition, in every trial, the average of all 13 electrodes was subtracted from the data. Because the raw traces exhibit strong 50 Hz noise due to the unusual ground electrode placement, the grand average of the red traces over all trials is also shown (blue trace). (E) Same data on a longer time scale. Note the similarity of the variety of the green traces to the artifacts in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006177#pcbi.1006177.g004" target="_blank">Fig 4A</a>. (F) On a log-log scale, the red follow a power-law with an exponent on the order of 1 (black dotted line). The green traces follow a power-law upon late-stage decay to baseline with an exponent on the order of 2 (black dashed lines).</p
Representative example of TMS artifacts on a human head and assessment of the artifact model.
<p>(A) Example of raw EEG traces displaying TMS-induced artifacts recorded from a human head. Magnetic stimulation was applied at time 0 at electrode Cz on a 64-electrode cap with 32 electrodes on the right hemisphere. The artifacts appear in every electrode trace at different strength or shape. Inset: On the uV scale of physiological brain waves, some traces exhibit an artifact duration of more than 100 ms. (B) The fast initial artifact dynamics related to the magnetic pulse. (C) Averaging out noise using five trials shows the long-lasting artifact decay to baseline. (D) On a log-log scale, the tails in the decay of the artifacts (from C) follow a power-law with an exponent on the order of 2 (red dashed lines). (E) TMS-EEG traces on a human knee. Shown are raw data (gray) of a single recording from 28 electrodes covering the knee following TMS. The artifacts reconstructed with the model are shown in green. (F) Log-log plot. (G) Data after subtraction of the reconstructed artifacts followed by subtraction of average of all traces to remove the common mode. As expected from TMS on a knee, the stimulation does not evoke neuronal activity, such that the artifact-removed traces are flat up to continuation of the typical very slow and small electrode drifts. The area shaded in gray indicates where the artifacts could not be reconstructed. (H) To assess the goodness of fit, we use the <i>Ļ</i><sup>2</sup>-test with significance level <i>Ī±</i> = 5%. Shown is the maximal time span for which the test accepts the fit. Beyond this time, the fit is rejected. Small electrode drifts and noise due to TMS-device recharging can shorten this time, however never below 20 ms. (I-J) Fits of sums of two exponentials. (K) Subtraction of the fits introduces both fast and slow distortions of the data in almost all traces. (L) Correspondingly, the fits are generally not accepted, except mainly in noisy and drifting electrodes. (M) The difference of data reconstructed by the model and by the sum of two exponentials. This equals the difference of the respective reconstructed artifacts. (N) For almost all fits by a sum of two exponentials, the quotients of the decay constants are approximately equal and have the same order of magnitude (<i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> constants, <i>t</i> time).</p
Equivalent circuits for the electrode-gel-skin interface.
<p>(A) Description of the electrode-skin-gel interface as lumped element model. The resistance and capacitance of the skin incorporate spatially varying properties. (B) Distributed circuit model for the spatial extent of the dermal interface. (C) The topology of a single-layer infinite regular grid with edge length <i>Ļµ</i>. A node <i>x</i> = (<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>) has four direct neighbors (<i>x</i><sub>1</sub>Ā±<i>Ļµ</i>, <i>x</i><sub>2</sub>), (<i>x</i><sub>1</sub>, <i>x</i><sub>2</sub>Ā±<i>Ļµ</i>). (D) The currents in direction <i>x</i><sub>1</sub> and <i>x</i><sub>2</sub> are denoted by <i>I</i><sub>1</sub> and <i>I</i><sub>2</sub>, respectively. Note that the injected current <i>J</i> is required to scale with <i>Ļµ</i>. (E) The voltages at the nodes are denoted by <i>V</i>.</p
The TMS-induced artifacts before and after skin preparation by puncturing and exfoliation.
<p>(A, B) Sample of raw EEG traces from a 64-electrodes cap after TMS application at CPz at time 0. Acquisition rate was 8 kHz to resolve the fast initial artifact dynamics. The recording before (red) and after skin puncture underneath the EEG electrodes (blue) shows no difference in the dynamics of the pulse artifact (A) but a reduction of the artifact decay (B). (C, D) Shown is the envelope (shaded area) of the two distributions of all artifacts before and after puncture. These distributions of artifacts were obtained by combining all sets of 64-electrodes cap traces from 2 subjects, each stimulated at both CPz and CP3 in a total of 71 TMS pulses. The pulse artifact is not changed (within an accuracy of one time step) by skin puncturing (C). The amplitude of the decay artifact (D) is reduced as shown by the shaded area, corresponding to the 5%-to-95% percentile of the distribution of all artifacts. (E) We compare two physical models of decay, (shifted) power laws <i>a</i>/(<i>t</i> + <i>b</i>)<sup>2</sup> and exponentials <i>c</i>exp(ā<i>dt</i>) (<i>t</i> time, <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> constants). Both models are least-squares fitted to all traces which do not change sign and have amplitude larger than 1.5 mV (dashed line). All fits are done to 25 ms starting from the point of reaching 1.5 mV. Evaluation of the fits by <i>R</i><sup>2</sup> shows the power law is better than the exponential with and without skin treatment. Specifically, skin puncturing does not decrease the difference of <i>R</i><sup>2</sup> by median (solid lines). (F-J) Same as (A-E) with skin exfoliation (green) instead of skin puncturing compared to control (red). Stimulation site was Cz and FP2, sampling rate 8 kHz.</p
The simulated voltage difference between a reference and the recording electrode.
<p>The initial voltage distribution at each electrode is a Gaussian of the form <i>g</i>(<i>Ļ</i>, <i>x</i> + <i>Ī¼</i>) convolved with the box function <i>B</i>, where <i>g</i>(<i>t</i>, <i>x</i>) is the voltage impulse-response function of our model, and <i>B</i>(<i>x</i>) equals 1/<i>Ļb</i><sup>2</sup> for |<i>x</i>| ā¤ <i>b</i>. The parameters for the reference electrode are fixed to <i>Ļ</i><sub><i>R</i></sub> = 0.5 and <i>Ī¼</i><sub><i>R</i></sub> = 0. The choice of <i>Ī¼</i><sub><i>R</i></sub> implies that the voltage depends only on the length |<i>Ī¼</i>| of <i>Ī¼</i> and not on its direction. The electrode radius was <i>b</i> = 2. (A, B) Effect of varying <i>Ļ</i> from 0 to 1 in steps of 0.05 (inset: close-up for <i>Ļ</i> for half step size). (D, E) Effect of varying |<i>Ī¼</i>| from 0 to 2 in steps of 0.1 (inset: close-up for |<i>Ī¼</i>| for half step size). (C, F) The plot on a log-log scale demonstrates the power law. In comparison to data, we note the asymmetry of positive and negative voltage shapes (compare to Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006177#pcbi.1006177.g004" target="_blank">4A</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006177#pcbi.1006177.g007" target="_blank">7A</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006177#pcbi.1006177.g011" target="_blank">11A</a>) and the emergence a local extremum near 0 in some traces (compare to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006177#pcbi.1006177.g004" target="_blank">Fig 4A</a>). (G-L) The simulated voltage difference for electrodes approximated by points (<i>b</i> = 0).</p
Comparison of excitation with a rotating vs. uni-directional field with and without the A-type channel blocker 4-AP.
<p>(A) Pulse durations needed for excitation with rotating (light green) vs. uni-direction (dark green) for [Ca2+] = 1 mM and [Mg2+] = 1 mM, similarly for [Ca2+] = 4 mM and [Mg2+] = 2 mM (center, light and dark blue) and for [Ca2+] = 4 mM and [Mg2+] = 2 mM with addition of 2 mM 4-AP (right, light and dark red). The effect of the change in concentration of ions is to decrease the membrane voltage, countering the increased excitability caused by blocking the A-type channels, which causes the durations needed to be overall about four times longer with higher ionic concentrations. (B) The ratios between durations needed for excitation with a rotating pulse and a uni-directional pulse for the three conditions measured: low concentrations of [Ca2+] and [Mg2+] (green), high concentration of [Ca2+] and [Mg2+] (blue), and high ionic concentrations with the addition of 4-AP (red). Addition of calcium and magnesium does not affect the ratio. Addition of 4-AP does shorten the duration of the uni-directional field but not of the rotating pulse.</p
Effect of changing the sampling rate.
<p>(A, B) Decreasing acquisition rate (16384 Hz, 8192 Hz, 4096 Hz, 2048 Hz, 1024 Hz) lead to a progressive time shift of the TMS artifacts and a decrease of TMS pulse artifact amplitude. The shifting time can be found by time-shifting the traces for each sampling rate backwards until they coincide with the 16 kHz traces. The optimal time is found when the sum of distances between these traces, evaluated directly after the pulse artifact, becomes minimal. The optimal times coincide for the watermelon and the human head (C). Note that time shifting will not change power law decay tails as can also be seen in (D).</p